Welcome to this experiment in decision-making. You will receive 5 Euros as a show- up fee. Please, read carefully these instructions. The amount of money you earn depends on the decisions you and other participants make. In this experiment, on top of the show-up fee, you can earn between 0 and 26.30 Euro. In the experiment you will earn ECU (Experimental Currency Units). At the end of the experiment we will convert the ECU you have earned into Euro according to the rate: 1 ECU = 0.7 EURO. You will be paid your earnings privately and confidentially after the experiment. Throughout the experiment you are not allowed to communicate with other participants in any way. If you have a question please raise your hand. One of us will come to your desk to answer it.
TASK 1
On the sheet of paper on your desk you see a puzzle: a matrix with 8 graphic elements and an empty slot. There are eight possible numbered elements that could fill the empty slot. Only one is correct. Your task is to identify the element that correctly solves the puzzle. You choose the element you want by typing the corresponding number and pressing OK.
You will face 36 such puzzles, divided in three blocks of 12 puzzles each. Within each block, you can move back and forth through puzzles even without solving them, and change the answers you have given before. You have five minutes to complete blocks 1 and 2, and eight minutes to complete block 3. For each puzzle you correctly solve you earn 0.1 ECU. You will be informed about your score and earnings at the end of the experiment.
FIGURE7: SCREENSHOT OF A QUESTION IN THERAVEN TEST
TASK 2
On the sheet of paper on your desk you see a field composed of 100 numbered boxes. You earn 0.1 ECU for every box that is collected. Every second a box is collected,
starting from the top-left corner. Once collected, the box disappears from the screen and your earnings are updated accordingly. At any moment you can see the amount earned up to that point.
Such earnings are only potential, however, because behind one of these boxes hides a time bomb that destroys everything that has been collected.
You do not know where this time bomb lies. You only know that the time bomb can be in any place with equal probability: the computer will randomly determine the number of the box containing the time bomb. Moreover, even if you collect the time bomb, you will not know it until the end of the experiment.
Your task is to choose when to stop the collecting process. You do so by hitting ’Stop’ at any time.
If you happen to have collected the box where the time bomb is located, you will earn zero. If the time bomb is located in a box that you did not collect you will earn the amount of money accumulated when hitting ’Stop’. We will start with a practice round. After that, the paying experiment starts.
FIGURE8: SCREENSHOT OF THEBOMB RISK ELICITATION TASK
In this part of the experiment, we model a procedure to allocate seats at schools to students. Each student has to submit an application form to apply for a seat at a school. You and the other participants take the role of students. An assignment pro- cedure that we will explain in detail below, decides, based on the application forms submitted by you and the other 15 participants, who receives a seat at which school.
There are 10 Rounds, in which you will apply anew for a seat at a school. All rounds are independent: where you are admitted, depends only on the application forms submitted in this round. Your chances in the current round are not influenced by your own decisions or the decisions of other participants in previous rounds. At the end of the experiment, one round is selected randomly. Your payoff for Task 3 depends on the school that you have been admitted to in that round.
Earnings: rounds 1-5
In each round, you and the remaining 15 participants apply for one of 16 seats. These are distributed over 4 schools – A, B, C, D – where each school has 4 seats. The earnings of a student admitted at a school depends on his type. There are 4 types of students – 1, 2, 3, 4 – with 4 students of each type. The type of a participant will be randomly drawn in each round. The earnings of a student, depending on his type and the school the he is admitted to, are summarized in the table below.
ECU for a seat at school A B C D
Type 1 20 10 6 0
Type 2 16 17 6 0
Type 3 16 10 8 0
Type 4 16 10 6 0
You can read the table as follows: in a round where you are a student of type 2 and are admitted at school C you earn 6 ECU - if this round is chosen to be paid out, this amount will be converted to Euros and paid out at the end of the experiment. In the same way, a student of type 3 that is admitted at school A receives a payoff of 16 ECU.
The payoffs above remain unchanged for the first 5 rounds. In rounds 6-10, there is different payoffs table, which you will see on the screen.
Available decisions
In each round, you have to submit an application form. To do so, you have to fill in under ‘first choice’, ‘second choice’, ‘third choice’ and ‘fourth choice’ the name of the respective school: ‘A’,‘B’,‘C’ or ‘D’. This ranking determines the order with which your applications are sent to the schools, and, through the procedure outlined below, the school you are assigned to. You are free to choose the order in which you rank schools. When you are done, confirm your list by clicking ‘submit’.
The assignment procedure [DA]
Once all application forms have been submitted, each student draws a lottery number from1to16: each number is drawn once. Each student has the same chances. For the assignment, students with a lower lottery number receive preferential treatment over students with a higher lottery number.
The assignment of participants to available seats works as follows: phase 1:
- Application by students. Each student applies at the school that he ranked as first
choice on his application form.
- Admission. If at most 4 students apply at a school, all of them are preliminarily
accepted. If more students apply at a school than the school has seats, the school preliminarily accepts the 4 students with the lowest lottery number. Applicants that do not receive a seat are permanently rejected at the respective school.
phase 2:
- Application by students. Every student, who has been accepted preliminarily in
round 1, still applies at the respective school. Every student that was rejected perma- nently in round 1, applies at the school that is next on his application form.
- Admission. Each school preliminarily accepts the 4 applicants with the lowest lot-
tery number. If there are less than 4 applicants, the school preliminarily accepts all applicants. Applicants that do not receive a seat are permanently rejected at the re- spective school.
phase 3:
- Application by students. Every student, who has been accepted preliminarily in
round 2, still applies at the respective school. Every student that was rejected perma- nently in round 2, applies at the school that is next on his application form.
- Admission. Each school preliminarily accepts the 4 applicants with the lowest lot-
tery number. If there are less than 4 applicants, the school preliminarily accepts all applicants. Applicants that do not receive a seat are permanently rejected at the re- spective school.
(. . . )
The procedure continues according to these rules. The procedure ends, once a phase is reached where every applicant is preliminarily accepted. In this moment, preliminary acceptance becomes permanent acceptance.
After every round you are informed about your lottery number and about the school where you received a seat. Then, the next round starts.
The assignment procedure [BOS]
Once all application forms have been submitted, each student draws a lottery number from1to16: each number is drawn once. Each student has the same chances. For the
assignment, students with a lower lottery number receive preferential treatment over students with a higher lottery number.
The assignment of participants to available seats works as follows: phase 1:
- Application by students. Each student applies at the school that he ranked as first
choice on his application form.
- Admission. If at most 4 students listed a school as first choice, all of them receive
a seat at that school. If more students listed a school as first choice, than the school has seats, the seats at that school are given to the students with the lowest lottery numbers. Students, who receive a seat in phase 1 are admitted for good; for them, the assignment procedure is over. Applicants that do not receive a seat move to the next phase.
phase 2:
- Application by students.Every student, who has not been assigned a seat in phase
1, applies at the school that he ranked as second choice on his application form.
- Admission. If in the second phase there are at most as many applicants as free seats
at the school, all of them receive a seat at the school. If there are more applicants than free seats, the remaining free seats are given to the students with the lowest lottery numbers. If there are no free seats left, no applicant receives a seat at the school. Students, who receive a seat in phase 2 are admitted for good; for them, the assignment procedure is over. Applicants that do not receive a seat move to the next phase.
phase 3:
- Application by students.Every student, who has not been assigned a seat in phases
1 and 2, applies at the school that he ranked as third choice on his application form.
- Admission. If in the third phase, there are at most as many applicants as free seats
at the school, everyone receives a seat at the school. If there are more applicants in the third phase than free seats, the remaining free seats are given to the students with the lowest lottery number. If there are no free seats left, no applicant receives a seat at the school. Students, who receive a seat in phase 3 are admitted for good; for them, the assignment procedure is over. Applicants that do not receive a seat move to the next phase.
phase 4:
- Application by students.Every student, who has not been assigned a seat in phases
1, 2 and 3, applies at the school that he ranked as fourth choice on his application form.
- Admission. Since there are 16 applicants and 16 seats, there are as many free seats
in phase 4 as applicants. Everyone receives a seat.
After every round you are informed about your lottery number and about the school where you received a seat. Then the next round starts.
Example [DA]
To illustrate the procedure described above, we consider an example. In this example, there are 8 students and 4 schools – V, W, X, Y – with 2 seats each to be assigned. Each Student draws a lottery number between1and8.
student Lottery number First choice Second choice Third choice Fourth choice 1 7 W V Y X 2 5 V W X Y 3 2 X V Y W 4 8 V X Y W 5 1 V Y W X 6 3 X W Y V 7 6 X W Y V 8 4 V Y X W phase 1:
- Student number 1 applies at his first choice, school W. Since he is the only applicant there for two seats, he is preliminarily accepted.
- Students number 2, 4, 5 and 8 apply at school V, that has only two seats available. The students with the two lowest lottery numbers (Students number 5 and 8) are preliminarily accepted at school V. Students number 2 and 4 receive no seat in this phase.
- Students number 3, 6 and 7 apply at school X, that also has two available seats. Since there are more applicants than available seats, students with the lowest lottery numbers (student number 3 and 6) are preliminarily accepted at X. Student number 7 receives no seat in this phase.
- Students number 1, 3, 5, 6 and 8 have been preliminarily accepted. Students number 2, 4 and 7 have received no seat in this phase. The procedure moves to the next phase. phase 2:
- Student number 2, 4 & 7 have no seat yet and apply at their second choice.
- Students number 2 and 7 apply at school W. Together with student number 1 who was preliminarily accepted there, there are now three applicants for two available seats. The school preliminarily accepts the applicants with the lowest lottery number (students number 2 and 7). Student 1, receives no seat in this phase.
- Student number 4 applies at school X. There, there are now three applicants, students number 3, 4, and 6, and only two seats. The school preliminarily accepts students number 3 and 6. Student number 4 receives no seat in this phase.
- Students number 1 and 4 have received no seat in this phase. The procedure moves to the next phase.
- Student number 1 applies at his second choice, school V. Together with the pre- liminarily accepted students number 5 and 8, there are now three applicants for two available seats. The school preliminarily accepts the applicants with the lowest lottery number, students number 5 and 8. Student 1 receives no seat in this phase.
- Student number 4 has been rejected twice and now applies at his third choice, school Y. There he is the only applicant and he is preliminarily accepted.
- Students number 1 has received no seat in this phase. The procedure moves to the next phase.
phase 4:
- Student number 1 applies at his third choice, school Y. Together with the preliminar- ily accepted student number 4, there are now two applicants for two available seats. The school accepts both.
- All Students have a preliminary acceptance at the end of the phase. The procedure stops; preliminary acceptances become permanent acceptances.
We arrive at the following assignment:
Student number 1 2 3 4 5 6 7 8
school Y W X Y V X W V
We start with a short quiz and an example. Then we begin with round 1.
Example [BOS]
To illustrate the procedure described above, we consider an example. In this example, there are 8 students and 4 schools – V, W, X, Y – with 2 seats each to be assigned. Each Student draws a lottery number between 1 and 8.
student Lottery number First choice Second choice Third choice Fourth choice 1 7 W V Y X 2 5 V W X Y 3 2 X V Y W 4 8 V X Y W 5 1 V Y W X 6 3 X W Y V 7 6 X W Y V 8 4 V Y X W phase 1:
- Student number 1 applies at his first choice, school W. Since he is the only applicant there for two seats, he is accepted.
- Students number 2, 4, 5 and 8 apply at school V, that has only 2 seats available. The students with the two lowest lottery numbers (Student number 5 and 8) are accepted at school A. Students number 2 and 4 receive no seat in this phase.
- Students number 3, 6 and 7 apply at school X, that also has two available seats. Since there are more applicants than available seats, students with the lowest lottery numbers (students number 3 and 6) are accepted at X. Student number 7 receives no seat in this phase.
- The assignment procedure ends for students number 1, 3, 5, 6, and 8, who all re- ceived a seat at a school. Students number 2, 4 and 7 have received no seat in this phase and move to the next phase.
phase 2:
- Students number 2, 4 & 7 have no seat yet and apply at their second choice.
- Students number 2 and 7 apply at school W, where there is one free seat available. This is assigned to the student with the lowest lottery number (student number 2). - Student number 4 applies at school X. There, there are no free seats.
- Students number 4 and 7 have received no seat in this phase and move to the next phase.
phase 3:
- Students number 4 and 7 apply at their third choice school, school Y, and are ad- mitted, as school D has two free seats available. With this, the assignment procedure ends.
We arrive at the following assignment:
Student number 1 2 3 4 5 6 7 8
school W W X Y V X Y V
We start with a short quiz and an example. Then we begin with round 1.